monthly lottery is a fun idea, we did/do that in our kin but def not on a regular basis or as frequent as your kin. you might want to try scavenger hunts, weekly deed or skirmish groups, if you have enough end game players, set up weekly raids, draigh, ToO, etc. you might set up crafting days, or if you have ppl that enjoy playing in game music, you can set up bands and sync your characters to play songs. things like this are always fun and get your kins morale pumping. hope this helps.
In my kin, we would do random things, such as Hide and Seek (either in a homestead or in the Breefield hedge maze) or random parties around holidays. For Halloween, we decided to do a dress up party with crazy costumes/outfits.
You could try setting up a weekly kin night, where you could run harder quests or instances for those who need it.
We had a kin on my server do a Follow the Leader during Bree. All the kin members lined up in a row behind the leader, and put the person in front of them on follow. It was kind of amusing. I hear they got new members from doing that.